It won't work without a high value feedback resistor like this: -
An op-amp integrator can never approach an ideal integrator because of the need to stabilize the DC output to somewhere near mid-rail and, that is what the resistor will do. Given that you have a 100 kΩ input resistor, you'll need something like 10 MΩ or greater as your feedback resistor.
The next problem is your input signal DC offset: -
An integrator does what it says on the tin - it will integrate the DC level of your signal and, it sounds like you don't want this to happen. So, you have to remove that DC level either with an offset adjustment circuit or a high pass filter. Maybe try this: -
Here's my simulation and note the time it takes to settle down to a reasonable DC mid-rail value. Note that I've run the AD822 from a +5 volt rail and not a +15 volt rail to make things clearer: -
If you lowered the 10 MΩ feedback resistor to 1 MΩ then the output waveform settles faster but, it just starts to show some minor triangle shape distortion: -
Maybe that would be OK?